The "digital revolution" that is transforming our lives and our economy is based on the ubiquity of information-processing devices whose processing power increased exponentially, following Moore's law. As this trend is approaching fundamental physical limits, new directions are explored for even more powerful computational devices based on quantum mechanical systems. Such devices can solve problems that will remain out of reach for conventional computers. The main difficulty for their implementation is the fragility of information stored in coherent superpositions of quantum mechanical eigenstates. This talk will highlight some aspects of the potential offered by quantum computers, as well as the difficulties that must be overcome to realise this potential. Our current work concentrates on finding solutions for some of these problems.

Photons, that is, the quanta of light fields, typically interact only weakly. In our research at the interface of quantum optics and condensed matter [1], we explore theoretically the behavior of quantum materials in which quantum light couples strongly and coherently to non-linear matter components. The matter, in turn, can mediate photon-photon interactions. Examples include dense optical media in optical cavities or fractionalized spins in quantum magnets, which couple to emergent gauge fields. In this talk, will describe our work on many-body physics across these areas and try to elucidate the differences and commonalities between the photons of quantum optics versus the emergent photons in strongly correlated condensed matter materials.

More than a century after the introduction of incandescent lighting and half a century after the realization of semiconductor lasers, semiconductor light sources are continuing to revolutionize applications and having a paramount impact on our everyday life. The creativity of quantum and photonics engineers and material scientists results in semiconductor light emitting diodes and semiconductor lasers with unprecedented characteristics, including ever better efficiency or brightness and ultra-wide wavelength coverage. In this talk, after a summary of general semiconductor laser research undertaken in our group, I will focus on the description of a novel kind of coherent light emitter based on a semiconductor microcavity with embedded quantum wells. In contrast to conventional lasers, this sort of device, termed polariton laser, relies not on stimulated emission of photons but on stimulated scattering of bosonic quasiparticles, the polaritons. These devices have lower thresholds than conventional lasers, and I will describe the physics underlying these devices and routes towards possible practical applications.

Ion traps are one of the promising platforms for quantum information processing and many proof of principle experiments have been realized with laser cooled trapped ions. A recent development is the application of inhomogeneous magnetic fields and microwave radiation for selective coherent manipulation and conditional dynamics. This allows for long coherence times and high fidelity one and two qubit gates, as demonstrated recently.

In this talk, I will focus on the storage, manipulation and readout of qubits encoded in the spin degree of freedom which can interact, upon application of an additional magnetic field gradient, by a magnetic gradient induced coupling (MAGIC). I will illustrate the concepts using results obtained with macroscopic and micro-structured traps, and compare to atomic qubits manipulated by optical means.

Synthetic quantum materials offer an exciting opportunity to explore quantum many-body physics and novel states of matter under controlled conditions. In particular, they provide an avenue to exchange the short length scales and large energy scales of the solid state for an engineered system with better control over the system Hamiltonian, more accurate state preparation, and higher fidelity state readout. Here we propose a unique platform to study quantum phases of strongly interacting photons. We introduce ideas for controlling the dynamics of individual photons by manipulating the geometry of a multimode optical cavity, and combine them with recently established techniques to mediate strong interactions between photons using Rydberg atoms. We demonstrate that this approach gives rise to crystalline- and fractional quantum Hall- states of light, opening the door to studies of strongly correlated quantum many-body physics in a photonic material.